A combinatorial algorithm for visualizing representatives with minimal self-intersection

TL;DR

This paper introduces a purely combinatorial algorithm that finds a representative with minimal self-intersection for a given free homotopy class on an orientable surface with boundary.

Contribution

It provides a novel combinatorial method to compute minimal self-intersection representatives, advancing topological visualization techniques.

Findings

Algorithm successfully minimizes self-intersections

Applicable to orientable surfaces with boundary

Efficient computational approach

Abstract

Given an orientable surface with boundary and a free homotopy class, we present a purely combinatorial algorithm which produces a representative of that homotopy class with minimal self intersection.